4x+x^2=250

Solution for 4x+x^2=250 equation:

4x+x^2=250

We move all terms to the left:

4x+x^2-(250)=0

a = 1; b = 4; c = -250;
Δ = b2-4ac
Δ = 42-4·1·(-250)
Δ = 1016
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1016}=\sqrt{4*254}=\sqrt{4}*\sqrt{254}=2\sqrt{254}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{254}}{2*1}=\frac{-4-2\sqrt{254}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{254}}{2*1}=\frac{-4+2\sqrt{254}}{2}
$